Osaka Journal of Mathematics

Twisted cohomology for hyperbolic three manifolds

Pere Menal-Ferrer and Joan Porti

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For a complete hyperbolic three manifold $M$, we consider the representations of $\pi_{1}(M)$ obtained by composing a lift of the holonomy with complex finite dimensional representations of $\mathrm{SL}(2,\mathbf{C})$. We prove a vanishing result for the cohomology of $M$ with coefficients twisted by these representations, using techniques of Matsushima--Murakami. We give some applications to local rigidity.

Article information

Osaka J. Math., Volume 49, Number 3 (2012), 741-769.

First available in Project Euclid: 15 October 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M50: Geometric structures on low-dimensional manifolds
Secondary: 20C15: Ordinary representations and characters


Menal-Ferrer, Pere; Porti, Joan. Twisted cohomology for hyperbolic three manifolds. Osaka J. Math. 49 (2012), no. 3, 741--769.

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